Time series are data observed over time (either in continuous time or at discrete time periods).

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Is there a method to disentangle multiple lines of data that are intermingled?

I have 3 temperature sensors that record data once a minute. All 3 temperatures have the tuple value (instant, temperature). The problem is, they may come in a random order and thus there's no way to ...
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1answer
35 views

prediction of polls

Just as an example Scotland has poll to decide whether they need to be independent from UK or not. Here is BBC's summary of different polls: ...
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4 views

Choose best time window to count events in order to produce an indicator

We want to create indicators for event based clinical conditions, like migraine or epilepsy. This conditions are characterized by events which can happen with various frequencies and we would like to ...
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1answer
40 views

Residual Value Prediction For Used Electronic Products

I am trying to predict the long term residual value of a product with only the releasing price. I have collected some data off the Internet related with one phone type, and it is pretty obvious that ...
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2answers
207 views

Average and standard deviation of timestamps (time wraps around at midnight)

I have lots of sensor data with timestamps like "2014-09-09 16:10:45" and accompanying sensor readings. To get some insight into these I want to find "unusual" events by looking at the average and ...
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14 views

Calculate standard error in state space model in R

I am estimating a DFM in state space form in R. I have used the function spg from the package BB (optim was not working) and dlm to optimize so now I have the parameters of the filter. I now would ...
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4answers
210 views

Forecast accuracy calculation

We are using STL (R implementation) for forecasting time series data. Every day we run daily forecasts. We would like to compare forecast values with real values and identify average deviation. For ...
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11 views

Sample autocovariance non negative definite

Let $\hat{\Gamma}_k$ be the k dimensional sample autocovariance matrix. I am trying to prove this is nonnegative definite. The first step in the proof is to show that if $\hat{\Gamma}_m$ is ...
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2answers
215 views

Test to distinguish periodic from almost periodic data

Suppose I have some unknown function $f$ with domain $ℝ$, which I know to fulfill some reasonable conditions like continuity. I know the exact values of $f$ (because the data comes from a simulation) ...
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30 views

Predicting one daily variable from another in SPSS

Note: There are similar questions to this one, but they don't seem to get at quite what I'm trying to figure out. I have a week's worth of daily data with a number of variables, including nighttime ...
2
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1answer
60 views

standard errors of the fitted values of a time series regression

I really want to understand how the math is working here. I am trying to get the standard error of the fitted values for a time series regression model.In the non-time series regression,I know I can ...
3
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1answer
90 views

Unable to understand derivation of Expectation Maximizaton

In Paper, System Identification using Symbolic Chaotic Sequence, Authored by A. Kurian and H. Leung download link under section II B, can somebody please explain ...
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55 views

Matlab: Unable to plot partial autocorrelation plot

For a time series I wanted to plot separately the partial auto correlation. Below is the graph for a time series which shows PACF plot of the time series $x$ which I wanted to reproduce: This ...
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1answer
40 views

How to solve this formula in R for specific days for the whole year? [closed]

I'm a beginner in R. I'd like to calculate the load for 3 water quality parameters in R for specific days for the whole year using the following formula: Using the previous formula, I'd like to ...
3
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2answers
143 views

How to estimate model with both linear and exponential parameters?

I have a theoretical growth function that can be perturbed by events, and I'd like to estimate the growth parameters as well as the perturbation, and the rate of falloff after that perturbation. I'm ...
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1answer
22 views

Is it still considered time series if one uses additional signals

Apologies in advance, time series is not my strength. Say I want to predict f(T+1) using f(T-1, T-2, ..., T-N) -- for example using a multi-level preceptron. If I want to enhance this using some ...
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1answer
32 views

Autocorrelation summation identity

Let $X_t$ be a weakly stationary process with mean $\mu$ and autocovariance function $\gamma$. How do I show that $$n^{-2}\sum_{i=1}^n \sum_{j=1}^n cov(X_i, X_j)$$ equals $$ n^{-2} \sum_{i-j=-n}^n ...
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28 views

Time Series Promotional Effectiveness

I'm trying to model the impact of two promotional tactics that ran in parallel for an year, I have the sales information at a month level and couple of metrics corresponding to the promotional tactics ...
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1answer
71 views

Product price prediction - include important external factors

I need some hint over what is the general prediction solution to modelling products prices in such a case: I have several models (types) of the product I want to predict prices for each of these ...
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22 views

Testing significance of a treatment inducing correlations over a time series

Example data In the example dataset, there are 3 distinct biological measurements, over 3 time points (0,12,24hrs) for 19 individuals. These individuals have been divided into 2 groups: treatment and ...
2
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1answer
47 views

Modeling time series data that is bimodal and non-Gaussian

I'm trying to model time series data that is bimodal and non-Gaussian. The 2 modes are due to weekday points versus weekend points. I keep thinking that I just need to split the data up to model ...
0
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1answer
43 views

Removing Time-Series Variance from Panel Data

We are working with panel data. But we want to study only the cross-section part of the panel data. So can anybody please tell me how to do any kind of data transformation, so that I can remove the ...
4
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4answers
184 views

Predicting time to finish

Out of curiosity, I want to understand how to model this problem. I've been hearing people suggest the use of linear regression but I am not sure how to encode this problem (included my attempt below) ...
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34 views

Rule of Thumb for minimum length of time series for Autocorrection estimation

I had a related question answered here: Rule of Thumb for minimum length of time series for AR(1) estimation However the answer gives rise to a new question. I want to be able to estimate the Auto ...
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0answers
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What is the error on measuring the phase of a sine wave? [duplicate]

Let's say I have a wave, with frequency $\omega$ and phase $\phi$, of the form: $$y(t)=1+A\sin(\omega t+\phi)$$ where $A<1$. I have $N$ measures of $(\hat{y}_i, \hat{t}_i)$, that are assumed to ...
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1answer
24 views

Data transformation

I was writing with a question regarding a time-varying state space model of the form: \begin{align} y(t) &= \mu_1(t) + A(t)x(t) + v(t); &v(t) &\sim (0, R(t)) \\ x(t) &= ...
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1answer
42 views

Rule of Thumb for minimum length of time series for AR(1) estimation

I have a data set of 350 points, I want to estimate the lag 1 auto correlation for different sub-sets of the data. More precisely I want to take non overlapping windows of length 1,2,3....n and ...
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21 views

Most efficient vector construction for Dynamic Time Warping

I'm in the process of folding FastDTW into my SVM and the question now is how to best format my data (irrespective of normalization). Here's an example of what I'm attempting to do - given two 3d ...
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33 views

Financial time series model

I have an interesting question that I think has not been asked yet here. I am building an AI that has as goal to predict how wrong a standard based-on-history model is. This is done based on Natural ...
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11 views

unconditional volatility from an Arma-Garch process

I know that one can easily get variance (unconditional) of a Garch (r,s) process : $\sigma^2= \frac { \alpha_0 } { (1- \Sigma_{i=1}^r \alpha_i - \Sigma_{j=1}^s \beta_j ) }$ However I am struggling ...
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1answer
60 views

How to fit an ARMAX model with more than one exogenous time series?

I am trying to fit an ARMAX with two exogenous time series with the following code but it gives me an "computationally singular" error. I know it is about defining more than 2 time series for ...
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15 views

What is the “scale” parameter in “continuous autoregressive model” in cts package?

I am trying to use the "car" command in "cts package" in R program and I see the "scale" parameter there. I wonder whether this can be assumed to be equivalent to time intervals for time series ...
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29 views

Bias in lagged dependent variable [duplicate]

$$ y_t = θy_{t−1} + u_t \\ t = 1,...,T; $$ I need to derive a formula for $y_t$ and show that $$ E\left[\frac{\Sigma y_{t-1}u_t}{ \Sigma(y_{t-1})^2}\right] \neq 0 $$
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1answer
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Modeling a non-stationary bounded series

I'm trying to model a time series variable that represents a percentage, strictly bounded between 0 and 1, that is also non-stationary about the mean. Is there a model form that is able to account ...
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14 views

Is time-delay embedding/attractor reconstruction used in some machine learning algorithm?

I try to model/forecast blood glucose levels from my diabetes diary, so I have to deal with some 5-7 daily measurements of estimated carbohydrates, physical activity, insulin doses and measured blood ...
3
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1answer
121 views

Doubts in linear regression

If a linear regression model has a constant term say 1 or 0.2, for example if the original model is $y(t) = 0.2 + ay(t-1) $, then what does this constant term imply? Will it hamper the estimates if ...
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Arima model for non-negative data

I have been reading a tutorial for an introduction to time series. It contains a dataset, with an $Arima(2,0,0)$ forecast along with a 80% and 95% prediction interval. It looks like this: This ...
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2answers
30 views

Confidence bands for difference of time series

Assume that I have two time series $Y_{1t}$ and $Y_{2t}$ that are sampled at the same frequency. Is there a way to quantify the uncertainty in their difference $Y_{1t} - Y_{2t}$? That is, can we get ...
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1answer
29 views

Testing the hypothesis on clustering

I have a number of samples. For each, there is a time course of multivariate data defined, with $t$ timepoints ($t < 50$) and $n$ variables ($n > 100$). We have noted that the time courses of a ...
2
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1answer
114 views

Can we skip the lower order terms in interactions? [duplicate]

This question is about three-way interaction and the possibility of applying without second lower terms with keeping the main variables in the equation not like the other questions. In fact the other ...
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3answers
69 views

Transforming time series to compensate for change in variance

I have a time series (shown below) that comes from a sensor whose calibration was changed in the middle of last year. As part of this change, the sensor's reading of the variance (or volatility) of ...
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0answers
24 views

Fitting a straight line to components of complex numbers

I have a strange problem that I'm not sure how to solve: I have complex data points in a time series. The amplitude of these complex numbers in the time series forms a straight line, which I have fit ...
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20 views

How to get observations from residuals in an ARIMA model?

If we have residuals of an ARIMA(p,d,q) with known parameters, how can we retrieve the original observations of the time series?
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42 views

Is two years enough for panel data analysis?

I have around 800 companies for only two years period. However, around 200 of them have only one year observation. Is it still possible to conduct panel data analysis with such data Thank you
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1answer
31 views

Is a Gaussian AR process with white noise independent?

I was just wandering if, given the AR process \begin{equation} X_t = \alpha X_{t-1} + \varepsilon_t, \quad \varepsilon_t \overset{iid}{\sim} N(0,1), \end{equation} the $X_t$ values are independent due ...
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50 views

State Space models with Short Time Series

My problem is that I have a state space model that I estimate using the Berndt–Hall–Hall–Hausman (BHHH) algorithm. The state space model is relatively simple in that the hidden part follows a pure ...
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51 views

Four tricky time series questions with a “seasonal twist”

A ski-hotel has the most guests in the third quarter in every year (check the data below after the four questions). Can you answer these four questions (every year has 4 values, the first is quarter ...
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37 views

Reproducing ARIMA error terms

When forecasting a moving average (MA) model using R's forecast, why does using residuals(fit) produce different results than ...
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20 views

What does it mean intuitively to say that a time series process is causal ?

What does it mean intuitively to say that a time series process is causal ? And what is the relationship between causality and stationary and invertibility ? If I understand correctly, these 3 ...
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1answer
31 views

Using Yule Walker equations for ACF and PACF

When using Using Yule Walker equations for getting ACF and PACF, is it essential that the time series has to be stationary? In other words, do we really need Box-Cox transformations before we use Yule ...